### Absolute distance measurement with micrometer accuracy using the

```Automated ADM with micrometer accuracy
using the Michelson interferometer
Coherent and Electro-Optics Research Group
(CEORG)
K Alzahrani, D Burton, M Lalor, F Lilley,
F Bezombes, and M Gdeisat
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Outlines
 Introduction
 Project objective
 Basic principles
 Michelson interferometer
 ADM using the Michelson interferometer
Challenges
Future work
Conclusion
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Introduction
Conventional interferometry can only determine relative
distance measurements – i.e. it can only determine how much
further away one point is compared to another point, provided
that both points are linked by a continuous path.
Absolute distance interferometry (ADI)can measure the
distance between any two arbitrary points.
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Project objective

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Building a fully automated ADM system, with micrometer
or better measurement accuracy, over comparatively large
distances of up to 40 meters.
Basic principles
Interference
Coherence length
Synthetic wavelength
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Interference
Light consists of burst of sine waves.
Two light waves derived from the same source and projected
onto a point may interfere if interference conditions have been
met.
The interference could be constructive or destructive.
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Interference
Similarly two light waves derived from the same source and
projected onto a surface may also interfere to produce fringes if
interference conditions have been met. As in Young’s double-slit
experiment.
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Coherence length
Light source emits light as
finite length trains.
The phase of the sine wave
changes randomly.
The distance between two
consecutive trains is called the
coherence length.
The longer the trains the more
coherent the light source.40 m
for the used laser.
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Synthetic wave
Two light waves with different
will become out of phase and then in
phase regularly. We refer to the length
over which this happens as synthetic
wavelength s .
s = (21/2-1 )
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Synthetic wave formation
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1 = 100nm, 2 =120nm
s =600nm
Michelson interferometer
construction
The Michelson interferometer produces interference fringes
by splitting a beam of monochromatic light so that one beam
strikes a fixed mirror and the other strikes a movable mirror.
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Michelson interferometer
Displacement measurement
In a conventional displacement measurement, laser
wavelength is held fixed and the interferometer system
counts fringes as a reflector is displaced.
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Michelson interferometer
scenario.1
Laser operates at a fixed wavelength .
 Let l1=l2, grab 1st image
to make l1≠l2,grab 2nd image
 There is a phase difference
between both patterns .
l =l1-l2
 l =0 then =0


l =  /4 then = π
 l =  /2 then = 2π
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Michelson interferometer
scenario.2.a
The arms of the interferometer is held fixed while the light
wavelength is changed.
Let l1=l2 , two fringe patterns are produces at 1 and 2.
 =0
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Michelson interferometer
scenario.2.b
Let l1 ≠ l2, laser operates at 1 and 2
Two fringe patterns are produced at 1 and 2.
There is a phase shift  between both fringe patterns.
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The algorithm
Suppose that we estimate lr and lm
and we know l with precision of
.
Laser operates at 1,grab 1st image
 Laser operates at 2,grab 2snd image
we can determine l with accuracy
of . Using the following equation
l= N s + f s where f=  /2π
Repeating this routine several times
with reduced  we will determine
l with increasing accuracy.
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Example
l ≃100mm,with  =0.5mm. 1 =685nm grab the 1st image.
 2 must satisfy the condition s = 2
 s = 1mm,δ =(1)/(s-1 )=0.47nm,2= 685.47nm
grab 2nd image
 measure  =1.9 rads (0.3 s )
 ΔL must lie between 99.5mm and 100.5mm
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N1=|l - /s | and N2=|l + /s | then N1=99 & N2=100.
Combining these to  and s, l 1 =99.3mm,l 2 =100.3mm.
 l 1 lies out of the tolerance range , therefore l =100.3mm
2nd iteration /2=0.25mm,l lies between two values with 0.5mm
difference. And according to N1 and N2 we choose one value that
falls in the tolerance range and so on.
Several iterations l can be determined with increasing accuracy.
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Algorithm flowchart
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Results
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System components
 A tunable laser with a tuning range of 680.4 nm to 691 nm.
 The wavelength can be changed with an accuracy of 0.1 nm.
 A wavelength meter with an accuracy of 0.0001 nm.
 A monochrome camera with a resolution of 1024X1360 pixels.
 Michelson interferometer.
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The absolute length measurement system
The system is completely controllable from the computer.
Using IDL software, we can set the tunable laser, read the
wavelength and grab fringe patterns in less than one second.
The tunable laser requires five seconds approximately to settle
down.
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Achievements
A significant amount of work has been put into
building the system and calibrating it.
An initial attempt was made to control the system
using a semi-automated approach and it was partially
successful.
With the semi-automated system, setting the laser,
reading the wavelength and grabbing an image takes
at least 10 minutes for each iteration.
The full iterative measurement process takes around
two hours.
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Achievements
Very recently, we managed to control the system
completely from the IDL software.
The system is now ready to use.
With the IDL system, setting the laser, reading the
wavelength and grabbing an image takes less than
one second.
The tunable laser requires five seconds
approximately to settle down.
The full iterative measurement process requires less
than 30 seconds.
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Future work
 The use of multi-wavelengths instead of two wavelengths will be
investigated.
 At the moment, we are able to measure the absolute distance for
one point with m accuracy. This capability will be extended to
measure the absolute distance for a surface.
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Conclusion
A new absolute length measurement system is proposed and a
patent application is underway for this system.
The hardware of the system has been built completely in
GERI labs from scratch and is completely automated using
IDL software.
The operation principle has been verified mathematically and
experimentally.
The system offers 4 micrometers or better measurement
accuracy over distances up to 40 meters.
Future work will be carried out to improve the performance
of this system and extend its capabilities.
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Thank you
Any Questions
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